Mean-field and Monte Carlo calculations of the equilibrium magnetic properties of uniaxial ferromagnetic particles

The low field magnetic properties of small uniaxial ferromagnetic particles are studied. We assume spherical particles, whose shells are inscribed into a simple cubic lattice. Each site of the sphere harbours a spin of the particle, which is represented by continuous vectors of unitary magnitude. The model is described by a classical Heisenberg model, where only nearest-neighbor interactions are taken into account. We employ mean-field calculations and Monte Carlo simulations to determine the magnetic properties of particles of different sizes, with radii ranging from three up to twelve lattice spacings. We consider the cases where the external magnetic field is applied along and perpendicularly to the easy axis of the particle. We determine the critical temperature as a function of the anisotropy and size of the particle. Monte Carlo calculations at low temperatures recover the Bloch law, showing that the magnetization decreases with a T3/2 law for isotropic particles larger than three spherical shells.